1. Let f(x) = x³ + x +1 for x E [0, 1]. Note that this function is continuous, increasing, invertible,Question 3and its range is [1, 3].1Determinef-(y) dy by relating this integral to| f(x) da geometrically.2. Suppose f is defined on [a, b] with range [c, d], is increasing, differentiable, and invertible. Use integration byparts to show that|f(y) dy = [bd – ac] – | f(x) dæ.-a3. Use part (b) to confirm your answer from part (a).

In the question we have to solve for function f(x)=x3+x+1 for x∈[0,1].

1. Let f(x) = ³ + x +1 for x E [0, 1]. Note that this function is continuous, increasing, invertible, Question 3 and its range is [1, 3]. Determine f-1(y) dy by relating this integral to f(x) dæ geometrically. 2. Suppose f is defined on [a, b] with range [c, d], is increasing, differentiable, and invertible. Use integration by parts to show that F(1) dy = [bd – ac] - | f(x) dr. 3. Use part (b) to confirm your answer from part (a).

1. Let f(x) = ³ + x +1 for x E [0, 1]. Note that this function is continuous, increasing, invertible, Question 3 and its range is [1, 3]. Determine f-1(y) dy by relating this integral to f(x) dæ geometrically. 2. Suppose f is defined on [a, b] with range [c, d], is increasing, differentiable, and invertible. Use integration by parts to show that F(1) dy = [bd – ac] - | f(x) dr. 3. Use part (b) to confirm your answer from part (a).

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter3: Functions

Section3.3: Rates Of Change And Behavior Of Graphs

Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...

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